X-ray diffraction is a non-destructive technique for the qualitative and quantitative analysis of crystalline material samples, which are generally provided in the form of single crystals or powders. In accordance with this technique, an X-ray beam is generated by an X-ray tube with a stationary anode, by a conventional rotating anode X-ray source or by a synchrotron source and directed toward the material sample under investigation.
When the X-ray beam strikes the sample, the X-rays produce Bragg angle reflections from the parallel and equally spaced atomic planes in the crystalline substance. Diffraction occurs if the path of the X-rays reflected by successive planes is a multiple of the X-ray wavelength. Therefore, the spacing between the atomic planes of a crystal can be determined by detecting the diffracted X-rays and measuring the first-order angles of diffraction. These measurements are usually performed by rotating the crystalline sample while taking diffraction measurements with a point X-ray detector.
Most conventional X-ray diffractometers use a Bragg-Brentano parafocusing geometry 100 such as that shown in FIG. 1. A divergent line-focus beam from the X-ray source 102 passes first through soller slits 1 (104) and the divergence slit 106, and then hits the sample surface 108 with an incident angle θ. The incident X-rays 110 spread over the sample surface 108 with various incident angles in the vicinity of θ. The area of the irradiated region depends on the incident angle θ and beam divergence. The diffracted X-rays 112 from the irradiated area leave the sample 108 at an angle 2θ from the corresponding incident rays, pass through an anti-scatter slit 114 and soller slits 2 (116) and focus at the receiving slit 118. A point X-ray detector 120 can be mounted at a position immediately after the receiving slit 118 or after a crystal monochromator 122 as shown in FIG. 1. The X-ray source 102, soller slits 104 and divergence slit 106 are all mounted on one arm of an instrument called a goniometer (not shown in FIG. 1). Similarly, the anti-scatter slit 114, the soller slits 116, the receiving slit 118, the monochromator 122 and the point detector 120 are all mounted on a second arm of the goniometer. The arms can be rotated or scanned around an instrument center point at which the sample 108 is located.
In this geometry, the beam-spread over the sample 108 varies with the incident angle θ, but the diffracted beam 112 is focused back to the receiving slit 118 as long as the axis of the X-ray source line focus and the receiving slit 118 are at the same distance from the instrument center (the goniometer main axis). This distance, R (124), is referred to as the “goniometer circle radius”.
A smaller aperture of the divergence slit 106 is used for higher 2θ resolution and a larger aperture for fast data collection. The Bragg-Brentano geometry requires that a normal to the sample surface 102 always bisect the angle between the incident beam 110 and the diffracted beam 112, that is the incident beam 110 and diffracted beam 112 are symmetric to the sample surface normal. This angular relationship can be achieved by scanning the goniometer arms at the same speed such that the angle between the X-ray source and the sample surface (θ1) always equals the angle between the X-ray detector and the sample surface (θ2) in a configuration called the “θ-θ configuration” or by holding the X-ray source stationary, rotating the sample at an angle ω and scanning the goniometer arm that holds the detector so that the angle 2θ increases at twice the speed of the angle ω in a configuration called the θ-2θ configuration.
Two-dimensional X-ray diffraction refers to X-ray diffraction applications that use an area X-ray detector and corresponding data reduction and analysis to produce a two-dimensional diffraction pattern and is described in detail in “Two-dimensional X-ray diffraction”, Bob B. He, John-Wiley and Sons, 2009. FIG. 2 shows the X-ray optics in a two-dimensional system 200 with a conventional θ-θ configuration. The X-ray tube 202, monochromator 204 and collimator assembly 206 are mounted on one of the two main axes of the system. In a conventional Bragg-Brentano diffraction system, a monochromator, such as monochromator 204, can be positioned either on the source side or the detector side, or both sides; however in a two-dimensional system, it is only possible to position the monochromator 204 on the source side. The incident beam 208 from the assembly 206 rotates about the instrument center and makes an incident angle θ1 from the sample surface 210. The first main axis of the system is also called the θ1 axis. The diffracted beams 212 travel in all directions and some are intercepted by a two dimensional detector 214 which is mounted on the other main axis of the system, θ2. The detector position is determined by the sample-to-detector distance D and the detector swing angle α(=θ1+θ2). In most two-dimensional diffractometers, the sample-to-detector distance can be changed manually or automatically.
In a two-dimensional X-ray diffraction system, since all, or a large portion, of the diffracted X-rays are measured simultaneously, the requirements for the X-ray optics are different from the conventional Bragg-Brentano diffractometer in many respects. In a two-dimensional system, the diffracted X-rays are measured simultaneously in a two-dimensional area so that neither the Bragg-Brentano geometry nor a conventional parallel geometry with detector soller slits can be used. The beam-spread over the sample surface cannot be focused back to the detector, so most of the time a collimated point beam is used. Therefore, X-ray optics for two-dimensional systems have different requirements in terms of the beam spectrum purity, divergence and beam cross-section profile.
In addition, a phenomenon called “air scatter” is also of more serious concern in a two-dimensional system than in a conventional diffractometer. Specifically, in diffractometers, all of the components and the space between the focal spot of the X-ray tube 202 and sample surface 210 are collectively referred to as the “primary beam path”. The space between the sample surface 210 and the two-dimensional detector 214 is referred to as the “secondary beam path”. The primary beam path in both conventional diffractometers and two-dimensional systems is typically sheltered by optical components except between the exit of the collimator 206 and the sample surface 210. The primary X-ray beam traveling through this open incident beam path is scattered by air in the path with two adverse effects. One is attenuation of the primary beam intensity. The more harmful effect is that the scattered X-rays travel in all directions and some reach the detector 214, as illustrated by the dotted lines 216 in FIG. 2. These scattered X-rays produce a background pattern which overlays the diffraction pattern produced by the sample. Weak diffraction patterns may be buried under the background pattern.
The diffracted X-rays are also scattered by air in the secondary beam path as indicated by the dotted lines 218 and the diffraction pattern is also both attenuated and blurred by this air scattering. However, air scatter effects from the primary beam are significantly stronger than that from secondary X-rays.
In a conventional diffractometer such as that shown in FIG. 1, an anti-scatter slit 114, diffracted beam monochromator 122 or detector soller slits 116 can be used to remove most of the air scatter not traveling in the diffracted beam direction. These measures cannot be used for a two-dimensional system, which requires an open space between the sample 210 and the two-dimensional detector 214. Radiation fluorescence is another source of intensity background in two-dimensional systems, especially when the X-ray energy of the incident beam is slightly higher than the absorption edge of the sample elements, for example, when Cu-Kα radiation is used for iron or ferrous alloys. In a conventional diffractometer with point detector, fluorescence can be removed by a diffracted beam monochromator 122, or an energy discrimination device, but this is not possible in two-dimensional systems.
Further, since the angle of the reflected X-rays cannot always be the same as the incident angle in a two-dimensional X-ray diffraction system, geometric aberrations are observed causing a defocusing effect. The defocusing effect occurs when the incident angle is lower than the reflection angle. FIG. 3 shows the geometry of two-dimensional diffraction in reflection mode with a flat sample 300. A parallel beam incident to the sample 302 is reflected and the resulting diffracted beam 304 is measured by a two-dimensional detector (not shown in FIG. 3). At low incident angles, the incident beam 302 spreads over the sample surface into an area much larger than the size of the incident X-ray beam 302. The observed diffracted beam size is magnified by the defocusing effect if the diffracted beam 304 occurs at an angle larger than the incident angle. Looking at the cross section on the diffractometer plane, the defocusing effect with reflection mode diffraction can be expressed as:
      B    b    =                    sin        ⁢                                  ⁢                  θ          2                            sin        ⁢                                  ⁢                  θ          1                      =                  sin        ⁡                  (                                    2              ⁢              θ                        -            ω                    )                            sin        ⁢                                  ⁢        ω            where θ1 is the incident angle, b is the incident beam size and B is diffracted beam size. The ratio of B to b is a measurement of the geometric aberration and will be referred to as the defocusing factor. For the Bragg-Brentano parafocusing geometry discussed above, with a divergence slit 106 and a receiving slit 118 of the same size, the defocusing factor is always 1 which implies no defocusing effect.
A two-dimensional diffraction pattern contains abundant information about the atomic arrangement, microstructure and defects of a solid or liquid material. Therefore, two-dimensional X-ray diffraction is an ideal, non-destructive, analytical method for examining samples of all kinds, such as metals, polymers, ceramics, semiconductors, thin films, coatings, paints, biomaterials, composite samples for material science research, molecular structure determination and polymorphism study for drug discovery and processing, and samples with micro-volume or micro-area for forensic analysis, archaeology analysis, and homeland defense as well as many emerging applications. Accordingly, in recent years, usage of two-dimensional diffractometer has dramatically increased in academic researches and various industries and it is desirable to have a two-dimensional system available.
On the other hand, although the Bragg-Brentano geometry has a slower data acquisition rate and has less information in the resulting diffraction pattern, the higher and controllable 2θ resolution, lack of a defocusing effect, and the possibility of effective shielding from air-scatter and fluorescence discrimination by a secondary monochromator makes it desirable sometimes to use the Bragg-Brentano geometry.
Due to the various differences between the Bragg-Brentano geometry and two dimensional systems, conventionally two separate systems are required in order to acquire data under optimal conditions. However, two separate systems double the expense; require a large operating area and personnel trained in the use of both systems.